Limits on differential rotation of the inner core from an analysis of the Earth's free oscillations

Differential rotation of the Earth's inner core has been inferred by several seismic ‘body-wave’ studies1,2,3,4,5,6 which indicate that the inner core is rotating at a rate between 0.2° and 3° per year faster than the Earth's crust and mantle. The wide range in inferred rotation rate is thought to be caused by the sensitivity of body-wave studies to local complexities in inner-core structure3,7. Free-oscillation ‘splitting functions’, on the other hand, are insensitive to local structure and therefore have the potential to estimate differential rotation more accurately. A previous free-oscillation study8, however, was equivocal in its conclusions because of the relatively poor quality and coverage of the long-period digital data available 20 years ago. Here we use a method for analysing free oscillations9 which is insensitive to earthquake source, location and mechanism to constrain this differential rotation. We find that inner-core differential rotation is essentially zero over the past 20 years (to within ±0.2° per year), implying that the inner core is probably gravitationally locked to the Earth's mantle10.